Volume 22, issue 5 (2018)

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Exotic open $4$–manifolds which are nonleaves

Carlos Meniño Cotón and Paul A Schweitzer

Geometry & Topology 22 (2018) 2791–2816
Abstract

We study the possibility of realizing exotic smooth structures on finitely punctured simply connected closed $4$–manifolds as leaves of a codimension-one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open $4$–manifolds which are not diffeomorphic to any leaf of a codimension-one ${C}^{2}$ foliation on a compact manifold. These examples include some exotic ${ℝ}^{4}$’s and exotic cylinders ${S}^{3}×ℝ$.

Keywords
exotic $\mathbb{R}^4$, nonleaves, codimension-one foliations
Mathematical Subject Classification 2010
Primary: 37C85, 53C12, 57R30
Secondary: 57R55